I'm going to assume the files are purchased/rented from iTunes that have the apple drm on them allowing them to only play in iTunes, iPods, iPads, and apple tvs. This may not be the case, and you may just have mov files (quicktime exclusive the plays in itunes and on apple products).
If the earlier is the case you may be SOL, although I think there are a few converters that basically play the drm movie/show in iTunes and record a copy as another file, though the quality goes down a bit. Not sure of the name of the tool though and I don't think its free. I beleive the company I saw it from was apple software producer ambrosia?
If the later is the case all you need to do is convert the files from mov to mpg, mpeg, m4v, etc that the S4 can use. At one time I think you could just change the mov extension to mpg and it would work, not sure if thats still the case.